Channel-Constrained Information Scheduling for Quantum Diffusion

Abstract:Information-based diffusion schedules organize the reverse problem by prescribing how much source information remains after each forward step. For mixed-state quantum diffusion, density-level targets need not correspond to trajectories reachable from the current realization. We introduce \emph{channel-constrained information scheduling}: each step optimizes over source-blind pure-state refinements reachable from the current state-resolved record through the prescribed channel. This defines a channel-constrained information clock $V_\xi$, whose inverse selects the least-corrupting step that reaches a target information level. Recursive inversion constructs a realizable equal-information schedule minimizing the worst source-information burden in Bayes reverse prediction. We establish attainment, continuity, monotonicity, convexity, finite support, and exact primal/dual formulations for $V_\xi$. We further give a sharp structural characterization: binary-qubit depolarizing trajectories attain the density-level Belavkin--Staszewski envelope, whereas every $d\ge3$ admits binary noncommuting families with a strict static--dynamic separation. Qutrit experiments show that the proposed scheduler nearly equalizes the realized multi-step burden, and learned reverse predictors recover the predicted allocation.

arXiv:2609.26273 [quant-ph]

(or arXiv:2609.26273v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.26273 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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